The force that is acting on the bodies is obtained as 1.15 * 10^- 48 N.
What is the force?Let us have it at the back of our minds that the force that is acting between the star and the planet has to be an attractive force since it is the force of gravity. Now we know that;
F = Gm1m2/r^2
F = force of gravity
m1 and m2 are the masses of the objects
r = The distance between the objects
Then;
F = 6.673x10^−11 * 6.1x10^30 * 4.8x10^7/(1.3x10^12)^2
F = 1.95 * 10^-24/1.69 * 10^24
F = 1.15 * 10^- 48 N
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the distance covered by a car at a time t is given by x=20t+6t^4. calculate the instantaneous velocity and acceleration when t= 1s.
Answer:
t = 1s is 44 m/s and 72 m/s^2
Explanation:
The distance covered by a car at a time t is given by x=20t+6t^4. To calculate the instantaneous velocity and acceleration when t=1s, we can use the formulas for velocity and acceleration, which are:
Velocity (v) = dx/dt = d/dt(20t+6t^4) = 20 + 24t^3
Acceleration (a) = dv/dt = d/dt(20 + 24t^3) = 72t^2
When t = 1s, we can substitute this value into the formulas for velocity and acceleration:
Velocity (v) = 20 + 24(1)^3 = 20 + 24 = 44 m/s
Acceleration (a) = 72(1)^2 = 72 m/s^2
Therefore, the instantaneous velocity and acceleration of the car when t = 1s is 44 m/s and 72 m/s^2, respectively.
Two equal masses are floating in space. The distance between their centers is X. How would the gravitational force between them change if the mass of one of the objects doubled?
A.The force would be the same.
B. The force would be one-fourth as much.
C. The force would be one-half as much.
D. The force would be twice as much.
The gravitational force between them would be twice as much.
option D is the correct answer.
What is Newton's law of universal gravitation?Newton's law of universal gravitation states that the force of attraction between two object in the universe is directly proportional to the product of their masses and inversely proportional to the square of the distance between the two objects.
Mathematically, the formula for Newton's law of universal gravitation is given as;
F = ( Gm₁m₂ ) / ( R² )
where;
m₁ is the mass of the first objectm₂ is the mass of the second objectR is the distance between the two objectsG is universal gravitation constantWhen mass of one of the objects doubles, the new gravitational force will be calculated as;
F' = ( Gm₁ x 2m₂ ) / ( R² )
F' = 2( Gm₁m₂ ) / ( R² )
F' = 2F
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OFFERING 80+ POINTS!!!!!!!!!
Three small spheres, A, B, and C, have charges with magnitudes qA, qB, and qC, respectively.The three spheres are aligned along a straight line, as shown in the figure. At the instant shown, the net force on sphere A is zero.:
1. Which of the following statements must be true of the signs of the charges?
a. Only charges qA and qB have the same sign.
b. Only charges qA and qC have the same sign.
c. Only charges qB and qC have the same sign.
d. Charges qB and qC have different signs.
e. Charges qA, qB, and qC all have the same sign.
2. The ratio qC/qB is...
a. 9/4
b. 1/1
c. 4/9
d. 1/4
e. 1/9
3. Which of the following is true about the sign of charge qA?
a. The sign of charge qA must be the same as that of qB.
b. The sign of charge qA must be the same as that of qC.
c. The sign of charge qA must be the same as that of either qB or qC greater magnitude.
d. The sign of charge qA must be the same as that of either qB or qC lesser magnitude.
e. It is possible that qA could be either positive or negative.
OFFERING A LOT OF POINTS FOR ANSWERS AND EXPLANATIONS TO ALL THREE!!
1. Charges qB and qC have different signs.
2. The ratio qC/qB is 9/4.
3. The sign of charge qA must be the same as that of either qB or qC lesser magnitude.
What is electric force?Electric force is the attracting or repulsive interaction between any two charged things. Similar to any force, Newton's laws of motion describe how it affects the target body and how it does so.
1. As net force on qA is zero, charges qB and qC have different signs.
2. The ratio qC/qB is = (3d)²/(2d)² = 9/4.
3. As the net force on qA is zero, the sign of charge qA must be the same as that of either qB or qC lesser magnitude.
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An observer in a truck observes a billboard appearing to move -21m/s to the east (east being in the +x direction), while a skater appears to be skating 24.94m/s 38 degrees north of west (north being in the +y direction, west in the −x direction). What is the velocity of the skater relative to the billboard?
The velocity of the skater relative to the billboard is 5.65 m/s east.
What is the velocity of the skater relative to the billboard?
The velocity of the skater relative to the billboard is the measure of the change in position of the skater with respect to the billboard. That is, how fast is the skater moving away from the billboard.
Considering the signs of east and west direction, the formula for the relative velocity of the Skater is given as;
Vs/B = Vs - VB
where;
Vs is the velocity of the skater with respect to the observerVB is the velocity of the billboard with respect to the observerThe magnitude of the velocity of the skater in west direction is given as;
Vs = V cos ( θ )
where;
V is the magnitude of the velocityθ is the angle of velocity of the skater with respect to x axisVs = 24.94 m/s x cos ( 90 - 38 )
Vs = 24.94 m/s x cos ( 52 )
Vs = 15.35 m/s
The velocity of the skater relative to the billboard is calculated as follows;
west = negative direction
east = positive direction
Vs/B = -15.35 m/s - ( -21 m/s )
Vs/B = 5.65 m/s
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A cone has a base radius of 3cm and height of 10cm.
A. Find the volume of the cone.
B. If the mass of the cone is 6kg, find its density.
The volume of the cone is 15.7 cm^3.
Density of cone is 0.38 kg/cm^3
Radius of the cone = 3 cm
Height of the cone = 10 cm
Formula used:
Volume of a cone = (1/3) × π × r^2 × h
Density is the measurement of how tightly a material is packed together. It is defined as the mass per unit volume. Density Symbol D or ρ Density Formula: ρ = m/V, where ρ is the density, m is the mass of the object and V is the volume of the object.
Where, r = radius of the cone
h = Height of the cone
Volume of the cone = (1/3) × π × r^2 × h
(1/3) × π × 3^2 × 10
(1/3) × (22/7) × 3^2 × 10
15.7 cm^3
Density = mass/volume
Density = 6kg/15.7 cm^3
Density = 0.38 kg/cm^3
Hence, the volume of the cone is
15.7 cm^3
And density of cone is 0.38 kg/cm^3
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The driver of a car traveling at 31.3 m/s applies the brakes and undergoes a constant
deceleration of 1.6 m/s^2.
How many revolutions does each tire make
before the car comes to a stop, assuming that
the car does not skid and that the tires have
radii of 0.31 m?
Answer in units of rev.
The distance the car travels before coming to a stop can be calculated using the equation d = (v^2 - u^2)/2a, where v is the initial velocity, u is the final velocity, and a is the acceleration.
What is acceleration?
Acceleration is the rate of change of velocity over time. It is defined as the rate at which an object's speed or direction changes with respect to time. Acceleration is a vector quantity, meaning it has both magnitude and direction.
The SI unit for acceleration is meters per second squared (m/s2). It is also commonly expressed in feet per second squared (ft/s2). Acceleration can be positive, negative, or zero. Positive acceleration occurs when an object increases its speed, and negative acceleration when it decreases its speed. Zero acceleration occurs when an object's speed remains constant.
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The figure below shows three small, charged spheres, all lying along the horizontal axis. Sphere A, at left, has a 5.10 nC charge. Sphere B has a 1.60 nC charge and is 3.00 cm to the right of A. Sphere C has a
−2.80 nC
charge and is 2.00 cm to the right of B.
Find the magnitude (in N) and direction of the net electric force on each of the spheres.
The magnitude and direction of the net electric force on each of the spheres is 1.92 x 10⁻⁵ N to the right.
What is the net electric force on the charges?The net electric force on the charges is calculated as follows;
F (net) = F (AB) + F (BC)
where;
F (AB) is the electric force between sphere A and BF (BC) is the electric force between sphere B and CThe electric force between sphere A and B is calculated as follows;
F ( AB ) = kq₁q₂ / r²
where;
q₁ is charge of sphere Aq₂ is charge of sphere Br is the distance between the two spheresK is Coulomb's constantF (AB) = ( 9 x 10⁹ x 5.1 x 10⁻⁹ x 1.6 x 10⁻⁹ ) / ( 0.03² )
F (AB) = 8.16 x 10⁻⁵
since it is between two positive charges, it will be repulsive, hence F (AB) = - 8.16 x 10⁻⁵
The electric force between sphere B and C is calculated as follows;
F (BC) = ( 9 x 10⁹ x 2.8 x 10⁻⁹ x 1.6 x 10⁻⁹ ) / ( 0.02² )
F (BC) = 1.008 x 10⁻⁴ N
since the force is between opposite charges, it will attractive, so F (BC) is positive.
The net force on each sphere is calculated as;
F (net) = -8.16 x 10⁻⁵ N + 1.008 x 10⁻⁴ N
F (net) = 1.92 x 10⁻⁵ N
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8. The time it takes a rock thrown straight up at 10 m/s to return to its starting position is about.
Answer: 2.04 Seconds
Explanation:Use t=(2v)/g = (2)(10)/9.8 = 2.04 seconds
the period of a simple pendulum increases by 50% when the length of the pendulum is increased by 0.6 m.
The intial length of the pendulum is
a) 1.2m
b) 0.48m
c) 0.24m
d) 0.12m.
Answer:
b) 0.48m is the right answer.
A 15 g toy car moving to the right at 22 cm/s
has a head-on nearly elastic collision with a
22 g toy car moving in the opposite direction
at 31 cm/s. After colliding, the 15g car moves
with a velocity of 42 cm/s to the left.
Find the speed of the second car after the
collision.
Answer in units of cm/s. Answer in units
of cm/s.
Answer:
Explanation:
The speed of the second car after the collision can be found using the law of conservation of momentum. The law states that the total momentum of a system remains constant if no external forces act on it.The initial momentum of the first car is (15g)(22 cm/s) = 330 g cm/s to the right.
The initial momentum of the second car is (22g)(-31 cm/s) = -682 g cm/s to the left.
The total initial momentum of the system is 330 g cm/s - 682 g cm/s = -352 g cm/sAfter the collision, the final momentum of the first car is (15g)(-42 cm/s) = -630 g cm/s to the left.
The final momentum of the second car is (m)(v) where m is the mass of the second car and v is the speed after the collision.
The total final momentum of the system is -630 g cm/s + (m)(v) = -352 g cm/s (since it remains constant)Therefore, m*v = -630 g cm/s + 352 g cm/s = -278 g cm/sTo find v, we need to divide the momentum by the mass
v = -278 g cm/s / 22 g = -12.6 cm/sSo the speed of the second car after the collision is -12.6 cm/s to the left.
20-mH inductor is connected across an AC source with a variable frequency and a constant-voltage amplitude of 9.0 V.
(a) Determine the reactance of the circuit and the maximum current through the inductor when the frequency is set at 20 kHz.
(b) Do the same calculations for a frequency of 60 Hz.
(a) At 20 kHz, the reactance of the inductor is X_L = 2πfL = 2π(20,000 Hz)(20 mH) = 1,256 Ω. The maximum current through the inductor is I_max = V/X_L = 9 V/1,256 Ω = 7.14 mA.
What is reactance?Reactance is an electrical phenomenon that occurs when an alternating current (AC) is applied to an inductive circuit. It is a type of opposition to the flow of electric current due to the inductance of the circuit. Reactance is measured in ohms and is the result of the inductive effect of the circuit components. When an AC voltage is applied to a circuit, the current that flows through the inductive circuit opposes the voltage change and produces an opposing voltage across the inductor which is called reactance.
(b) At 60 Hz, the reactance of the inductor is X_L = 2πfL = 2π(60 Hz)(20 mH) = 377 Ω. The maximum current through the inductor is I_max = V/X_L = 9 V/377 Ω = 23.87 mA. At lower frequencies, the reactance of the inductor is lower, so the current through the inductor is higher.
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Eve's
contractor recommended she not install baseboard heating. In which scenario would it be disadvantageous to install a baseboard heating system?
A. Where there is high room air circulation
B. Where there are low ceiling heights
C. Where electricity is generated from a gas-fired plant
D. Where the TD is zero
Mark for review (Will be highlighted on the review page)
Installing an underfloor heating system in a situation where the electricity is generated by a gas-fired plant would not be advantageous.
What is electricity exactly?Charge or electrical supply flow is what is referred to as electricity. It is an alternative fuel source, which means we obtain it by transforming other natural resources into energy supplies, such as carbon, dirty energy, hydrocarbons, and nuclear energy.
How does electricity get made?To create electricity, a turbine set converts mechanical energy into electrical energy. The heat produced by sources of energy such natural gas, carbon, nuclear reactors, biomass, petroleum, volcanic, and solar heat is employed to transform to steam, which powers the rotors of turbines.
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An asteroid is in a highly eccentric elliptical orbit around the Sun. The period of the asteroid’s orbit is 90 days. Which of the following statements is true about the possibility of a collision between this asteroid and the Earth? (a) There is no possible danger of a collision. (b) There is a possibility of a collision. (c) There is not enough information to determine whether there is danger of a collision
About the possibility of a collision between this asteroid and the Earth the true statement is there is not enough information to determine whether there is danger of a collision.
What is asteroid?
A tiny, stony object called an asteroid orbits the Sun. They are made up of materials left over from the formation of the solar system and are typically found in the asteroid belt. Most asteroids are less than one kilometer in diameter, but some can be much larger. Asteroids are commonly composed of minerals and metals, such as iron, magnesium, and silicon. Asteroids are classified into three main types: C-type, S-type, and M-type. C-type asteroids are the most common and make up around 75% of known asteroids. They are made up of dark, carbon-rich material and are often referred to as "carbonaceous chondrites". S-type asteroids are made up of silicate material, such as clay and silica, and are typically brighter than C-type asteroids. M-type asteroids are made of metallic material, such as iron and nickel, and are the least common type.
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A SpaceX Crew Dragon with a mass of 5,000 kg is approaching the International Space Station (ISS). The mass of the ISS is 420,000 kg. The table below shows the magnitude of the gravitational forces each object exerts on each other at various ranges:
Range Force on Crew Dragon Force on ISS
1 km 1.4 E−7 N 5.4 E−8 N
500 m 5.6 E−7 N 1.3 E−6 N
200 m 3.5 E−6 N 3.5 E−6 N
100 m 1.4 E−5 N 1.4 E−7 N
Which of the following table entries is correct for their interaction?
A. 1 km
B. 500 m
C. 200 m
D. 100 m
C. 200 m
The gravitational force between two objects is determined by the mass of each object and the distance between them. The gravitational force is inversely proportional to the square of the distance between the objects and directly proportional to the product of the masses. The gravitational force exerted by the ISS on the Crew Dragon is equal in magnitude but opposite in direction to the force exerted by the Crew Dragon on the ISS.
In the table provided, at a range of 200 m, the force on the Crew Dragon is 3.5 E-6 N and the force on the ISS is 3.5 E-6 N, showing that the forces are equal and opposite in direction. At other ranges, the force on the Crew Dragon and the force on the ISS are not equal, this means that the gravitational force at 200m is correct for their interaction.
3 A uniform plank of weight 120N rests on two stools as
shown in Fig. 5.16. A weight of 80N is placed on the
plank, midway between the stools. Calculate:
a the force acting on the stool at A,
b the force acting on the stool at B.
I’m confused on how to calculate moment of weight if there are two pivots
The force acting on the stools of the 88N and 112N.
What is meant by force?
An external force is an agent that has the power to alter the resting or moving condition of a body. It has a direction and a magnitude.The application of force is the location at which force is applied, and the direction in which the force is applied is known as the direction of the force.The word "force" has a specific meaning in science.At this level, calling a force a push or a pull is entirely appropriate.A force is not something an object "has in it" or that it "contains." One thing experiences a force from another.There are both living things and non-living objects in the concept of a force.A uniform plank of weight 120N rests on two stools as a midway between the stool.
(80 × 1.25) + (120 × 1.5) = B × 2.5
B = 112N
80 × 1.25) + (120 × 1.0) = A × 2.5
A = 88N
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.
A hot rod of mass 1200 kg, starting from rest
reaches a speed of 110 m/s in only 18.3 s.
What is the average output power?
The average output power of the hot rod is 793,442.62 W.
What is the average output power?
The average output power is calculated by applying the following equation for average power.
P = Fv
where;
F is the average force applied by the objectv is the velocity of the objectBut force, F = ma
where;
a is the acceleration of the objectm is the mass of the objectP = ( ma ) x ( v )
P = ( m x v/t ) x ( v )
P = ( mv² ) / ( t )
where;
t is the time of motion
The average output power of the hot rod is calculated as follows
P = ( 1200 x 110² ) / ( 18.3 )
P = 793,442.62 W
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At which location would a bowling ball have the greatest weight? on Earth, at the top of a tall mountain on the surface of the moon on Earth, several kilometers below the surface on Earth at sea level
Several Kilometres below the earth at Sea level
.
Without changing the size of the applied force or the small piston, how can you increase the amount of force that comes out of a hydraulic lift?
One way to increase the amount of force that comes out of a hydraulic lift is by increasing the area of the larger piston. Since pressure is equal to force divided by area, if the area of the larger piston is increased, the pressure on the larger piston will be less, but the force will remain the same. This means that the force applied to the small piston will be amplified on the larger piston, resulting in a greater force being exerted by the larger piston.
Another way to increase the amount of force that comes out of a hydraulic lift is by decreasing the area of the small piston. As in this case the pressure is same on both pistons but the force would be more on the small piston and thus will be amplified to a greater force on the larger piston.
By using both methods together, the effect of increasing the force that comes out of a hydraulic lift is even greater.
Alexa exerts a force of 560 N on the
ground, due to her weight.
a) When Alexa is wearing high-heeled
shoes, the total area of her shoes in
2
contact with the ground is 58 cm².
When she has bare feet, the total area of
her feet in contact with the ground is
230 cm².
2
Calculate the difference between the
pressure she exerts on the ground when
she is wearing these shoes and when she
has bare feet.
Give your answer in N/cm² to 1 d.p.
Answer:
[tex]\Delta P \approx 7.2 \ N/cm^2}[/tex]
Explanation:
To calculate the difference in pressure that Alexa exerts on the ground when wearing high-heeled shoes compared to when she has bare feet, we can use the following formula for pressure:
[tex]\rightarrow P=\dfrac{F}{A}[/tex]
Where:
"F" is the force exerted in the ground."A" is the area the force is applied to.First, let's calculate the pressure when Alexa is wearing high-heeled shoes:
F = 560 N (given)
A = 58 cm² (given)
[tex]P_h=\dfrac{560}{58}\\\\\\\\\therefore P_h \approx 9.655 \ N/cm^2[/tex]
Next, let's calculate the pressure when Alexa has bare feet:
F = 560 N (given)
A = 230 cm² (given)
[tex]P_b=\dfrac{560}{230}\\\\\\\\\therefore P_h \approx 2.435 \ N/cm^2[/tex]
Finally, let's calculate the difference in pressure:
[tex]\Delta P= P_h-P_b\\\\\\\\\Longrightarrow \Delta P =9.655-2.435\\\\\\\\\therefore \boxed{\boxed{\Delta P \approx 7.2 \ N/cm^2}}[/tex]
Therefore, the difference in pressure that Alexa exerts on the ground when wearing high-heeled shoes compared to when she has bare feet is approximately 7.2 N/cm².
A runner whose initial speed is 29 km/h increases her speed to 31 km/h in
order to win a race. If the runner takes 5.0 seconds to complete this
increase in her speed, what is her acceleration?
I need this answered asap!!!
The acceleration of the runner is 0.12 m/s^2.
What is the acceleration?We have to note that the term acceleration would have to do with the rate of the change of the velocity of the object with time. Now we have to note that in this case, we would have to change the velocities of the body to the unit of meter per second.
Initial velocity = 29 km/h or 8 m/s
Final velocity = 31 km/h or 8.6 m/s
We then have that;
a = v - u/t
Then we can be able to substitute the values and have;
a = 8.6 - 8/5
= 0.12 m/s^2
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It’s 2:00pm. The local weather station is tracking a violent storm that is traveling east at 25 km/hr. It is 75km west of Ft. Collins. Daniel starts riding his bike home at 5:00. Will he be home before the storm hits?
To determine whether Daniel will be home before the storm hits, we need to determine the time it will take for the storm to reach Fort Collins and compare it to the time it will take for Daniel to reach home by bike.
Given:
Storm's speed = 25 km/hr = 25000 m/hr
Distance from Fort Collins = 75 km = 75000 m
Time of storm = distance / speed = 75000 m / 25000 m/hr = 3 hrs
If Daniel starts riding his bike home at 5:00pm, he needs to cover the distance from where he is to his home before the storm hits Fort Collins.
If he is able to maintain an average speed of 20km/h = 20000 m/h,
time = distance/speed = 75000 m/20000 m/h = 3.75 hrs
Since the storm will take 3 hours to reach Fort Collins and Daniel will take 3.75 hours to reach home by bike, he will be home before the storm hits.
what does air resistance do when an object falls
Answer:slows it down
Explanation:when something drops it slow down
Answer: increase
Explanation: Air resistance is increases with velocity. When object fall , the velocity will increase. so, resistance will increase.
A student solving a physics problem to find the unknown has applied physics principles and obtained the expression: μkmgcosθ=mgsinθ−ma , where g=9.80meter/second2 , a=3.60meter/second2 , θ=27.0∘ , and m is not given. Which of the following represents a simplified expression for μk ?
The simplified expression for the coefficient of kinetic friction is 0.097.
What is the coefficient of kinetic friction?The coefficient of kinetic friction is described as the ratio of the kinetic friction force of contacting surfaces to the normal force.
The simplified expression for the coefficient of kinetic friction is calculated as follows;
μkmgcosθ = mgsinθ − ma
m(μkgcosθ) = m(gsinθ − a)
μkgcosθ = gsinθ − a
μk= gsinθ − a/ gcosθ
where;
μk is the coefficient of kinetic friction g is the acceleration due to gravityθ is the anglea is the acceleration of the objectWe have the given parameters:
g = 9.8 m/s²
a = 3.6 m/s²
θ=27.0∘
μk = (9.8 sin 27.0 ) - 3.6 / 9.8 cos27.0
μk = 0.097
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If I have a BEYBLADE spinning for about 34 seconds, how many mph does it spin? If I have a BEYBLADE that spins for 42 seconds, how many mph does it spin?
34 second beyblade speed= 1 rotation every 00.1 second
42 second beyblade speed= 1 rotation every 0.00001 second
These are estimated speeds. I think this because the speed of the beyblade.
the information provided (34 and 42 seconds) does not give the necessary information to determine the speed at which the BEYBLADE is spinning in miles per hour. To calculate the speed of the BEYBLADE we need to know the distance traveled in each rotation. Also, you mentioned that the beyblade makes 1 rotation in 34 seconds and 42 seconds, which is not correct, it should be 1 rotation per second in 34 seconds, and 1 rotation per 42 seconds.
7. In order to determine the power dissipated across a resistor, the current flow and resistance values are measured separately. If I = 3.2 A and R = 10000. Instrument Uncertainty (% of reading) Voltmeter 0.5% Ohmmeter 0.1% Ammeter 0.5% . Power can be measured as P = l²R or P = VI. Which method will give the most accurate measurement?
The method that will give the most accurate measurement is P = l²R, because it has the least uncertainty.
What is the power dissipated in a circuit?
The power dissipated in a circuit is given by the following formula as shown below.
P = I²R
P = VI
where;
I is the current flowing in the circuitV is the voltage drop in the circuitR is the resistance of the circuitPercentage uncertainty gives the error associated with each measurement. The greater the value of percentage uncertainty, the greater the error associated with the measurement.
To determine the method that will given the most accurate measurement, we will find out the method with least error.
For the first method, = I²R
uncertainty in measurement of current = 0.5 % Ammeteruncertainty in measurement of resistance = 0.1 %uncertainty in measurement of voltage = 0.5 %Total uncertainty for first method = I²R = ( 0.5 % )² x ( 0.1 % ) = 0.0025%
Total uncertainty for second method = VI = ( 0.5% x 0.5 % ) = 0.25 %
Thus, the measurement with the least uncertainty is the first method, I²R.
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The space shuttle Copernicus is docking with an orbiting space station for refueling. Copernicus has a mass of 20,000 kg and approaches the station with a speed of 50 m/s . The space station has a mass of 80,000 kg and is floating toward the space ship with a speed of 10 m/s . How fast will Copernicus and the space station be moving after they have successfully docked? *Hint* remember that the direction of speed matters.
Copernicus and the space station will be moving at 2 m/s after they have successfully docked.
What is law of conservation of momentum?According to the law of conservation of momentum, absent an external force, the combined momentum of two or more bodies operating upon one another in an isolated system remains constant.
From law of conservation of momentum, we can write:
Total initial momentum = Total final momentum
80000 kg × (- 10 m/s) + 20000 kg × (+ 50 m/s) = (80000 kg + 20000 kg) × (v m/s)
v = 2 m/s.
Hence, Copernicus and the space station will be moving at 2 m/s after they have successfully docked.
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A stone is thrown into the air. Its height above the ground t seconds after it is thrown is given by
the function h(t) = -5t² + 30t+2 metres.
How high is the stone above the ground at time t = 3 seconds?
b From what height above the ground was the stone released?
At what time is the stone 27 m above the ground?
Answer:
Explanation:
a) To find the height of the stone above the ground at time t = 3 seconds, we need to substitute t = 3 into the function h(t) = -5t² + 30t + 2 and solve for h(3).
h(3) = (-53²) + (303) + 2 = -45 + 90 + 2 = 37m
b) To find from what height above the ground the stone was released, we need to find the value of h(0), which represents the height of the stone at time t = 0, which is the time the stone was released.
h(0) = (-50²) + (300) + 2 = 2 m
c) To find the time at which the stone is 27 m above the ground, we need to solve for t in the equation h(t) = 27.
27 = (-5t²) + (30t) + 2
27 = -5t² + 30t + 2
25 = -5t² + 30t
5t² - 30t - 25 = 0
(5t-5)(t+5) = 0
t = 1 or t = -5
As time cannot be negative, the time at which the stone is 27 m above the ground is t = 1 sec.
The following equation estimates the average calories burned for a person when exercising, which is based on a scientific journal article (source):
Calories = ( (Age x 0.2757) + (Weight x 0.03295) + (Heart Rate x 1.0781) — 75.4991 ) x Time / 8.368
Write a program using inputs age (years), weight (pounds), heart rate (beats per minute), and time (minutes), respectively. Output the average calories burned for a person.
Output each floating-point value with two digits after the decimal point, which can be achieved as follows:
print('Calories: {:.2f} calories'.format(calories))
Ex: If the input is:
Here is an example of a Python program that calculates the average calories burned for a person based on the equation provided:.
def calories_burned(age, weight, heart_rate, time):
calories = ((age * 0.2757) + (weight * 0.03295) + (heart_rate * 1.0781) - 75.4991) * time / 8.368
return calories
age = int(input("Enter your age in years: "))
weight = int(input("Enter your weight in pounds: "))
heart_rate = int(input("Enter your heart rate in beats per minute: "))
time = int(input("Enter the duration of your exercise in minutes: "))
print("You have burned an average of", calories_burned(age, weight, heart_rate, time), "calories.")
What is the program about?This program defines a function calories_burned() that takes four inputs: age, weight, heart rate, and time. The function then uses the provided equation to calculate the average calories burned and returns the result.
The program also prompts the user to enter their age, weight, heart rate, and time, and then prints the result of the calculation.
Learn more about program on:
https://brainly.com/question/26642771
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a ball is projected with initial velocity 40m/s at angle of 27° from a building 60meters high.find total time the ball is in the air
Answer:
projectile motion
total time of flight= 2V° Sintheta / g
answer is 3second
Hope This would help you!
How much power does it take to lift 30.0 kg 10.0 m high in 5 seconds
Answer:
About 600 watts
Explanation:
Work = force x distance = 30 x 10 x 10 = 3000 J. Power = Work done/time = 3000/ 5 = 600 watts.
